Problem: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2}{x - 2} = \dfrac{-7x + 18}{x - 2}$
Solution: Multiply both sides by $x - 2$ $ \dfrac{x^2}{x - 2} (x - 2) = \dfrac{-7x + 18}{x - 2} (x - 2)$ $ x^2 = -7x + 18$ Subtract $-7x + 18$ from both sides: $ x^2 - (-7x + 18) = -7x + 18 - (-7x + 18)$ $ x^2 + 7x - 18 = 0$ Factor the expression: $ (x + 9)(x - 2) = 0$ Therefore $x = -9$ or $x = 2$ However, the original expression is undefined when $x = 2$. Therefore, the only solution is $x = -9$.